Retrieving shallow shear-wave velocity profiles from 2D seismic-reflection data with severely aliased surface waves

The inversion of surface-wave phase-velocity dispersion curves provides a reliable method to derive near-surface shear-wave velocity profiles. In this work, we invert phase-velocity dispersion curves estimated from 2D seismic-reflection data. These data cannot be used to image the first 50 m with seismic-reflection processing techniques due to the presence of indistinct first breaks and significant NMO-stretching of the shallow reflections. A surface-wave analysis was proposed to derive information about the near surface in order to complement the seismic-reflection stacked sections, which are satisfactory for depths between 50 and 700 m. In order to perform the analysis, we had to overcome some problems, such as the short acquisition time and the large receiver spacing, which resulted in severe spatial aliasing. The analysis consists of spatial partitioning of each line in segments, picking of the phase-velocity dispersion curves for each segment in the f-k domain, and inversion of the picked curves using the neighborhood algorithm. The spatial aliasing is successfully circumvented by continuously tracking the surface-wave modal curves in the f-k domain. This enables us to sample the curves up to a frequency of 40 Hz, even though most components beyond 10 Hz are spatially aliased. The inverted 2D VS sections feature smooth horizontal layers, and a sensitivity analysis yields a penetration depth of 20–25 m. The results suggest that long profiles may be more efficiently surveyed by using a large receiver separation and dealing with the spatial aliasing in the described way, rather than ensuring that no spatially aliased surface waves are acquired.Fil: Onnis, Luciano Emanuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Osella, Ana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Itali

Linear stationary point problems on unbounded polyhedra

Stationary Point

Classification Under Misspecification: Halfspaces, Generalized Linear Models, and Connections to Evolvability

In this paper we revisit some classic problems on classification under misspecification. In particular, we study the problem of learning halfspaces under Massart noise with rate $\eta$. In a recent work, Diakonikolas, Goulekakis, and Tzamos resolved a long-standing problem by giving the first efficient algorithm for learning to accuracy $\eta + \epsilon$ for any $\epsilon > 0$. However, their algorithm outputs a complicated hypothesis, which partitions space into $\text{poly}(d,1/\epsilon)$ regions. Here we give a much simpler algorithm and in the process resolve a number of outstanding open questions: (1) We give the first proper learner for Massart halfspaces that achieves $\eta + \epsilon$. We also give improved bounds on the sample complexity achievable by polynomial time algorithms. (2) Based on (1), we develop a blackbox knowledge distillation procedure to convert an arbitrarily complex classifier to an equally good proper classifier. (3) By leveraging a simple but overlooked connection to evolvability, we show any SQ algorithm requires super-polynomially many queries to achieve $\mathsf{OPT} + \epsilon$. Moreover we study generalized linear models where $\mathbb{E}[Y|\mathbf{X}] = \sigma(\langle \mathbf{w}^*, \mathbf{X}\rangle)$ for any odd, monotone, and Lipschitz function $\sigma$. This family includes the previously mentioned halfspace models as a special case, but is much richer and includes other fundamental models like logistic regression. We introduce a challenging new corruption model that generalizes Massart noise, and give a general algorithm for learning in this setting. Our algorithms are based on a small set of core recipes for learning to classify in the presence of misspecification. Finally we study our algorithm for learning halfspaces under Massart noise empirically and find that it exhibits some appealing fairness properties.Comment: 51 pages, comments welcom

Time-lapse inversion of Controlled Source Electromagnetics using vertical sources and receivers

Knowledge of spatial and temporal distribution of fluids in the subsurface is crucial in a wide range of applications. During the production of crude oil typically high saline produced formation water is injected into the reservoir layer, aiming to push the oil towards production wells. While oil is commonly seen as an electrical insulator, the injected saline brines are characterised by low electrical resistivity. Thus, electromagnetic (EM) methods and especially Controlled Source Electromagnetics (CSEM) attracted an increasing interest to monitor these resistivity changes inside the reservoir over time. This thesis mainly reports on numerical aspects of modelling and inversion of land based CSEM with particular focus towards hydrocarbon monitoring applications. Most of the presented developments were inspired by a superordinate research project including CSEM field surveys across an actively producing onshore oil field in Northern Germany. In producing oil fields there exists a large number of steel-cased wells. Such existing oil field infrastructure and especially the presence of metal casings significantly alters the propagation of EM fields in the subsurface. Their spatially unfavourable dimensions effectively prohibits a straightforward implementation into the modelling grid. Thus I developed a new modelling approach allowing consideration of such thin but vertically extended highly conductive structures including their mutual interaction. The developed methodology had been implemented into existing modelling and inversion codes. Using the new approach to investigate the influence of metal casings on CSEM data shows that they act as additional inductively coupled vertical electric dipole sources at depth and thereby increase resolution capabilities at depth. The presence of metal casings can thus be exploited by optimising the source receiver layout in such a way that the strength of these additional vertical dipole sources is maximised. An additional working package of the superordinate project was the measurement of vertical electric fields in a shallow observation well. However, measurements of vertical electric fields requires long measurement dipoles to achieve satisfactory signalto- noise ratios. Such extended dipoles span several modelling cells and are therefore in conflict with assumptions usually made for modelling, that receivers can be represented as point dipoles. I therefore expanded the modelling and inversion codes to consider the physical receiver dimensions. The new algorithm implicitly considers imperfect alignment of the receiver with the corresponding field component. Without the consideration of this effect inversion of vertical electric field measurements is likely to cause erroneous results. Finally I discuss different aspects of time-lapse inversion required to track changes in fluid saturation over time. The cascaded inversion scheme is applied to synthetic timelapse data for a simplified oilfield undergoing brine flushing. The influence of various inversion parameters in particular different regularisation techniques are examined. Surface based sources and receivers typically provide low sensitivity towards deep targets in highly conductive backgrounds. Despite that using additional constraints, in particular a model weighting scheme together with energised steel casings allowed to track resistivity changes inside the reservoir based on synthetic time-lapse data.Wissen über räumliche und zeitliche Verteilung von Fluiden im Untergrund is unerlässlich für eine Reihe von Anwendungen. Typischerweise wird während der Förderung von Rohöl salinares produziertes Formationswasser in die ölführende Formation injiziert um das Öl-Wasser-Gemisch in Richtung der Förderbohrungen zu spülen. Während Öl als elektrischer Isolator gilt, zeichnen sich die injizierten salinaren Fluide durch eine hohe elektrische Leitfähigkeit aus. Daher erfahren elektromagnetische Methoden und insbesondere Controlled Source Electromagentics (CSEM) zunehmendes Interesse diese Änderung des elektrischen Widerstands mit der Zeit zu überwachen. Diese Arbeit beschäftigt sich im wesentlichen mit numerischen Aspekten der Modellierung und Inversion von CSEM an Land mit speziellem Fokus auf der Überwachung der Kohlenwasserstoff Produktion. Die meisten der gezeigten Entwicklungen sind entwickelt im Zuge eines übergeordneten Forschungsprojektes inklusive CSEM Feldmessungen in einem produzierenden Ölfeld in Norddeutschland. Produzierende Ölfelder sind gekennzeichnet durch eine große Anzahl von Stahl verrohrten Bohrungen. Die Anwesenheit von Stahlinfrastruktur insbesondere von Stahlschutzrohren beeinflusst die Ausbreitung von elektromagnetischen Feldern im Untergrund. Deren unvorteilhafte Geometrie erlaubt keine direkte Berücksichtigung in dem Modellierungsgitter. Daher habe ich einen neuen Modellierungsanzatz entwickelt der es erlaubt solch dünne aber vertikal ausgedehnte hochgradig leitfähige Strukturen inklusive deren gegenseitige Wechselwirkung zu berücksichtigen. Die entwickelte Methode wurde in bestehende Modellierungs- und Inversionssoftware implementiert. Mithilfe dieses neuen Ansatzes konnte der Einfluss von Stahlverrohrungen auf CSEM Daten untersucht werden. Stahlverrohrungen wirken wie zusätzliche induktiv angeregte vertikale elektrische Dipolquellen im Untergrund und helfen daher die Auflösung in der Tiefe zu erhöhen. Die Anwesenheit von Stahlverrohrungen kann daher ausgenutzt werden in dem man die Quell-Empfänger-Geometrie in einer Art und Weise optimiert, die die Stärke dieser zusätzlichen vertikalen Dipolquellen maximiert. Ein weiteres Arbeitspaket des übergeordneten Forschungsprojektes bestand in der Messung von vertikalen elektrischen Feldern in flachen Beobachtungsbohrungen. Messungen des vertikalen elektrischen Feldes erfordert lange Messdipole um ein ausreichendes Signal-Rausch-Verhältnisses zu gewährleisten. Solch ausgedehnte Dipole überspannen mehrere Zellen des Modellierungsgitters und verletzen die übliche Annahme, wonach die Länge der Empfänger vernachlässigbar ist. Daher habe ich die bestehenden Modellierungs- und Inversionsprogramme erweitert um die physischen Dimensionen von elektrischen Feld Empfängern zu berücksichtigen. Der implementierte Algorithmus berücksichtigt implizit Abweichungen der Orientierung des Messdipols von der Richtung der zu messenden Feldkomponente. Ohne dieser Berücksichtigung führt eine Inversion von vertikalen elektrischen Feld Daten zu fehlerhaften Ergebnissen. Schließlich werden unterschiedliche Aspekte von time-lapse Inversion diskutiert, welche notwendig ist um Änderungen der Fluidzusammensetzung abzubilden und zu verfolgen. Eine kaskadiertes Inversionsschema wurde auf synthetische time-lapse Daten eines vereinfachten Ölfeldes angewendet. Untersucht wurde der Einfluss verschiedener Parameter insbesondere verschiedener Regularisierungstechniken. Sender und Empfänger an der Erdoberfläche sind typischerweise wenig sensitiv zu tiefen Strukturen in leitfähiger Umgebung. Anhand von synthetische Daten konnte gezeigt werden, dass das benutzen zusätzlicher Nebenbedingungen wie einer Modellgewichtung und dem ausnutzen von vorhandenen Stahlverrohrungen es dennoch erlaubt Änderungen innerhalb des Ölreservoirs zu lokalisieren

Time-varying networks: Measurement, Modeling, and Computation

Time-varying networks and techniques developed to study them have been used to analyze dynamic systems in social, computational, biological, and other contexts. Significant progress has been made in this area in recent years, resulting from a combination of statistical advances and improved computational resources, giving rise to a range of new research questions. This thesis addresses problems related to three lines of inquiry involving dynamic networks: data collection designs; the conditions needed for structural stability of an evolving network; and the computational scalability of statistical models for network dynamics. The first contribution involves a commonly neglected problem concerning data collection protocols for dynamic network data: the impact of in-design missingness. A systematic formalization is offered for the widely used class of retrospective life history designs, and it is shown that design parameters have nontrivial effects on both the quantity of missingness and the impact of such missingness on network modeling and reconstruction. Using a simulation study, we also show how the consequences of design parameters for inference vary as a function of look-back time relative to the time of measurement. The second contribution of this thesis is related to a fundamental question of network dynamics: when or where are changes in a network most likely to occur? A novel approach is taken to this question, by exploring its complement -- what factors stabilize a network (or subgraphs thereof) and make it resistant to change? For networks whose behavior can be parameterized in exponential family form, a formal characterization of the graph-stabilizing region of the parameter space is shown to correspond to a convex polytope in the parameter space. A related construction can be used to find subgraphs that are or are not stable with respect to a given parameter vector, and to identify edge variables that are most vulnerable to perturbation. Finally, the third contribution of this thesis is to scalable parameter estimation for a class of temporal exponential family random graph models (TERGM) from sampled data. An algorithm is proposed that allows accurate approximation of maximum likelihood estimates for certain classes of TERGMs from egocentrically sampled retrospective life history data, without requiring simulation of the underlying network (a major bottleneck when the network size is large). Estimation time for this algorithm scales with the data size, and not with the size of the network, allowing it to be employed on very large populations

CLADAG 2021 BOOK OF ABSTRACTS AND SHORT PAPERS

The book collects the short papers presented at the 13th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS). The meeting has been organized by the Department of Statistics, Computer Science and Applications of the University of Florence, under the auspices of the Italian Statistical Society and the International Federation of Classification Societies (IFCS). CLADAG is a member of the IFCS, a federation of national, regional, and linguistically-based classification societies. It is a non-profit, non-political scientific organization, whose aims are to further classification research